Which of these numbers is prime? ${75,\ 81,\ 83,\ 84,\ 93}$
A prime number has exactly two factors: 1 and itself. The factors of 75 are 1, 3, 5, 15, 25, and 75. The factors of 81 are 1, 3, 9, 27, and 81. The factors of 83 are 1 and 83. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. The factors of 93 are 1, 3, 31, and 93. Thus, 83 is a prime number.